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Applied Mathematics-A Journal of Chinese Universities  2018, Vol. 33 Issue (1): 25-34    DOI: 10.1007/s11766-018-3522-z
    
Waiting times and stopping probabilities for patterns in Markov chains
ZHAO Min-zhi1, XU Dong1, ZHANG Hui-zeng2
1 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China. Email: zhaomz@zju.edu.cn, xudong 1236@163.com
2 Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China. Email: zhanghz789@163.com
Waiting times and stopping probabilities for patterns in Markov chains
ZHAO Min-zhi1, XU Dong1, ZHANG Hui-zeng2
1 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China. Email: zhaomz@zju.edu.cn, xudong 1236@163.com
2 Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China. Email: zhanghz789@163.com
 全文: PDF 
摘要： Suppose that $\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\mathcal C$ occurs as a run. This time is denoted by $\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\tau)$ and the stopping probabilities $P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time until the pattern $A$ appears as a run.
关键词： pattern;  Markov chain;  stopping probability;  waiting time    
Abstract: Suppose that $\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\mathcal C$ occurs as a run. This time is denoted by $\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\tau)$ and the stopping probabilities $P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time until the pattern $A$ appears as a run.
Key words: pattern    Markov chain    stopping probability    waiting time
收稿日期: 2017-01-13 出版日期: 2018-03-28
CLC:  60J10  
基金资助: Supported by the National Natural Science Foundation of China (11771286, 11371317) and by the Zhejiang Provincial Natural Science Foundation of China (LQ18A010007).
通讯作者: ZHANG Hui-zeng     E-mail: zhanghz789@163.com
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引用本文:

ZHAO Min-zhi, XU Dong, ZHANG Hui-zeng. Waiting times and stopping probabilities for patterns in Markov chains[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 25-34.

ZHAO Min-zhi, XU Dong, ZHANG Hui-zeng. Waiting times and stopping probabilities for patterns in Markov chains. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 25-34.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-018-3522-z    或    http://www.zjujournals.com/amjcub/CN/Y2018/V33/I1/25

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